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Two groups of 40 runners each run 400 m…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two groups of 40 runners each run 400 m. The median time of group B is faster than the lower quartile of group A. Faster means a smaller time. At least how many runners in group B ran faster than the lower quartile of group A? About how many runners in group A ran faster than their own lower quartile? Write one sentence that compares the groups.
Need a reminder? The key ideaShow
Compare groups by centre (median), spread (IQR and range), shape and outliers, on one shared axis. A median above the other group's means at least half of one group is above about three quarters of the other.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Group B. At least half of group B, 20 runners, ran faster than B's median. That median is faster than A's lower quartile, so at least 20 runners of B beat A's lower quartile.
Step 2. Group A. About a quarter of group A, 10 runners, ran faster than A's own lower quartile.
Answer: at least 20 runners and about 10 runners.
A sentence. At least half of group B ran faster than all but about a quarter of group A, so group B was typically much faster.
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